From Kefalonia, Greece. There are ferries run by Blue Sea Travel which will take you from the Port Sami in Kefalonia into Ithaca, Port Vathi. The ship is called 'Sami Star I'. It costs (at 09 June 2013) 25€ return for an adult. The ship departs for Ithaca at 08:45 and returns to Sami at 17:00. The route runs every Saturday, Tuesday and Thursday. The trip takes 30 to 40 minutes. There's plenty of free parking for cars around Sami. Strinzis Travel run car ferries across to Ithaca too. There are taxis in Ithaca however you'll find little or no public transport other than "Shanks' Pony" (your legs :-).
Ithaca is the legendary home of the Greek poet Homer's heroic Odysseus. There are various sites that are associated with this legendary figure including a cave said to honor this mythical hero at Polis Bay.